Kolmogorov-Smirnov Test - what are the exact alternative hypotheses?
I have performed the Kolmogorov-Smirnov test (ks.test) with R the first
What I am not sure about is the exact alternative hypotheses (H1) given
According to Conover (1971) Practical Nonparametric Statistics, chapter
6, the following one-sample tests can be performed:
(1) Two-sided test
H0: F(x) = F*(x)
H1: F(x) =/= F*(x) [for at least one x]
(2) one-sided test
H0: F(x) =< F*(x)
H1: F(x) > F*(x) [for at least one x]
H0: F(x) >= F*(x)
H1: F(x) < F*(x) [for at least one x]
with F(x) being the empirical distribution of sample data and F*(x) the
hypothesised distribution. F*(x) requires full specification, which can
be achieved by "fitdistr(..., F*(x)).
The KS Test on R tests a sample performs a 2-sided test as default mode.
The choice for "alternative" seems to allow for a choice of H0 different
to the standard of two-sided.
Suppose one would chooses "less" or "greater" as "alternative". Does the
KS test automatically set the correct H1?
Whenever I perform the test, the alternative hypothesis is not being
stated, that is why I am not certain whether I would be correct to make
Here is an example of the output for a test:
P*(x) is a lognormal distribution, fully specified with meanlog and sdlog.
> ks.test(spread,plnorm, meanlog=2.359, sdlog=0.588, alternative =